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  27 <a name="boost.accumulators.impl.kurtosis_impl"></a><div class="titlepage"></div>
  28 <div class="refnamediv">
  29 <h2><span class="refentrytitle">Struct template kurtosis_impl</span></h2>
  30 <p>boost::accumulators::impl::kurtosis_impl &#8212; Kurtosis estimation. </p>
  31 </div>
  32 <h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
  33 <div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: &lt;<a class="link" href="../../../accumulators/reference.html#header.boost.accumulators.statistics_fwd_hpp" title="Header &lt;boost/accumulators/statistics_fwd.hpp&gt;">boost/accumulators/statistics_fwd.hpp</a>&gt;
  34
  35 </span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Sample<span class="special">&gt;</span>
  36 <span class="keyword">struct</span> <a class="link" href="kurtosis_impl.html" title="Struct template kurtosis_impl">kurtosis_impl</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">accumulator_base</span> <span class="special">{</span>
  37   <span class="comment">// <a class="link" href="kurtosis_impl.html#boost.accumulators.impl.kurtosis_implconstruct-copy-destruct">construct/copy/destruct</a></span>
  38   <a class="link" href="kurtosis_impl.html#idp411100544-bb"><span class="identifier">kurtosis_impl</span></a><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span><span class="special">;</span>
  39
  40   <span class="comment">// <a class="link" href="kurtosis_impl.html#idp411097168-bb">public member functions</a></span>
  41   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="identifier">result_type</span> <a class="link" href="kurtosis_impl.html#idp411097728-bb"><span class="identifier">result</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  42 <span class="special">}</span><span class="special">;</span></pre></div>
  43 <div class="refsect1">
  44 <a name="idp115238032"></a><h2>Description</h2>
  45 <p>The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central moment (the variance) of the samples, minus 3. The term <span class="inlinemediaobject"><img src="../../../images/accumulators//form_12.png"></span> is added in order to ensure that the normal distribution has zero kurtosis. The kurtosis can also be expressed by the simple moments:</p>
  46 <div class="equation">
  47 <a name="idp115241552"></a><p class="title"><b>Equation&#160;1.16.&#160;</b></p>
  48 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_13.png" align="middle"></div></div>
  49 </div>
  50 <p><br class="equation-break"></p>
  51 <p>where <span class="inlinemediaobject"><img src="../../../images/accumulators//form_14.png"></span> are the <span class="inlinemediaobject"><img src="../../../images/accumulators//form_15.png"></span>-th moment and <span class="inlinemediaobject"><img src="../../../images/accumulators//form_16.png"></span> the mean (first moment) of the <span class="inlinemediaobject"><img src="../../../images/accumulators//form_17.png"></span> samples. </p>
  52 <div class="refsect2">
  53 <a name="idp115254528"></a><h3>
  54 <a name="boost.accumulators.impl.kurtosis_implconstruct-copy-destruct"></a><code class="computeroutput">kurtosis_impl</code>
  55         public
  56        construct/copy/destruct</h3>
  57 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><a name="idp411100544-bb"></a><span class="identifier">kurtosis_impl</span><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span><span class="special">;</span></pre></li></ol></div>
  58 </div>
  59 <div class="refsect2">
  60 <a name="idp115261056"></a><h3>
  61 <a name="idp411097168-bb"></a><code class="computeroutput">kurtosis_impl</code> public member functions</h3>
  62 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="identifier">result_type</span> <a name="idp411097728-bb"></a><span class="identifier">result</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span> args<span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre></li></ol></div>
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  68 <td align="right"><div class="copyright-footer">Copyright &#169; 2005, 2006 Eric Niebler<p>
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  70         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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